In The Crucible how does Miller portray male/female relationships, in particular between Betty and Parris?
If you look at the key male/female relationships in the play, you might start to wonder if Miller really meant to portray such negative, heated interactions between the two.
Let's look at Betty and her father, Reverend Parris. Betty is so terrified of getting in trouble by her father that she becomes, almost literally, paralyzed by fear. He discovered her dancing in the woods, and knew that most definitely she would be whipped, and maybe more if the "other stuff" was discovered. Fear of her father makes her go inert, pretending illness instead of having to face him. This relays male/female relationships as fraught with a dominant male and a cowering female.
Then, let's look at John and Abby. These two obviously, at one point, had a very passionate relationship--one based mostly on lust, probably, but it soon turns sour when John ends it. John feels bitterness towards her in the end, and she pines after him--her desire for him drives her to drastic actions. So, we see a love/hate relationship develop between the two; Miller seems to portray this one as a firey, but overall destructive and negative relationship.
Next is John and Elizabeth. Miller portrays their relationship as fraught with distrust, negativity, criticism, careful words, and explosive arguments. Elizabeth is a cold, critical woman and John is resentful and prideful; his affair still interferes in their happiness. However, in this relationship, there is hope. In the closing act of the play, Miller shows them in a tender moment of reconcilation and love; he seems to be saying that marriage can be hard, but it is worth it to fight through challenges.
The other relationship that we can infer from is that of Mr. Putnam and Ruth; later, Ruth is prompted, through her father, to accuse an innocent man of witchcraft, so that he can get the man's land. This shows an overpowering father figure again, with a girl willing to please and do what he says, no matter the repercussions.
I hope that those analyses help a bit; good luck!